Quantum kinetic theory of irreversible thermodynamics: Low-density gases

A quantum theory of irreversible thermodynamics is developed for a system of dilute quantum particles in terms of an irreversible kinetic equation for the density matrix, which is assumed to have a structure similar to the Boltzmann-Nordheim-Uehling-Uhlenbeck equation. The local balance equations for conserved variables (mass, momentum, and energy) and the evolution equations for nonconserved variables are derived directly from the density matrix. They have the same mathematical structures as the corresponding classical equations. It is shown that the local entropy differential consists of a compensation differential and an energy dissipation term that depends on the path of irreversible processes in the macroscopic variable space, as in the case of the corresponding classical system. The statistical definition of temperature for nonequilibrium systems and its operational meaning are discussed in detail. The extended hydrodynamic equations are presented, which attend the theory of irreversible processes and are consistent with the H theorem. Application of the theory is briefly discussed.